How do I upgrade my operating system to Yosemite on a MacBook Air running Lion 10.7.5? I don't have 2Gb memory free.

Assuming you previously purchased it from the app store and your Mac meets the minimum requirements, you offload enough data to an external drive to free up the required disk space and update via the app store. If you didn't previously purchase it and it's not listed in your purchases list, you don't.